SIAM Journal on Scientific and Statistical Computing
Variants of BICGSTAB for matrices with complex spectrum
SIAM Journal on Scientific Computing
A Sparse Approximate Inverse Preconditioner for the Conjugate Gradient Method
SIAM Journal on Scientific Computing
Matrix market: a web resource for test matrix collections
Proceedings of the IFIP TC2/WG2.5 working conference on Quality of numerical software: assessment and enhancement
Parallel resolvent Monte Carlo algorithms for linear algebra problems
Mathematics and Computers in Simulation - IMACS sponsored Special issue on the second IMACS seminar on Monte Carlo methods
Preconditioning Highly Indefinite and Nonsymmetric Matrices
SIAM Journal on Scientific Computing
Mixed Monte Carlo Parallel Algorithms for Matrix Computation
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Factorized Sparse Approximate Inverses for Preconditioning
The Journal of Supercomputing
Parallel algorithms for Markov chain Monte Carlo methods in latent spatial Gaussian models
Statistics and Computing
Solving Linear Equations by Monte Carlo Simulation
SIAM Journal on Scientific Computing
Monte Carlo methods for matrix computations on the grid
Future Generation Computer Systems
An efficient parallel implementation of the MSPAI preconditioner
Parallel Computing
The university of Florida sparse matrix collection
ACM Transactions on Mathematical Software (TOMS)
A sparse parallel hybrid monte carlo algorithm for matrix computations
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part III
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This paper presents a Monte Carlo SPAI pre-conditioner. In contrast to the standard deterministic SPAI pre-conditioners that use the Frobenius norm, a Monte Carlo alternative that relies on the use of Markov Chain Monte Carlo (MCMC) methods to compute a rough matrix inverse (MI) is given. Monte Carlo methods enable a quick rough estimate of the non-zero elements of the inverse matrix with a given precision and certain probability. The advantage of this method is that the same approach is applied to sparse and dense matrices and that complexity of the Monte Carlo matrix inversion is linear of the size of the matrix. The behaviour of the proposed algorithm is studied, its performance is investigated and a comparison with the standard deterministic SPAI, as well as the optimized and parallel MSPAI version is made. Further Monte Carlo SPAI and MSPAI are used for solving systems of linear algebraic equations (SLAE) using BiCGSTAB and a comparison of the results is made.